ANALYTICAL MECHANICS
xj', yO denotes the position and v' the velocity of PI with pect to X'PzY', we get
ferentiating the last two equations with respect to the te
refore
= (xi + yi) — (x2 + ya = vi-v2.
(V)
jation (V) states that the velocity of a particle with :>ect to another particle is obtained by subtracting the )city of the first from that of the second.
ILLUSTRATIVE EXAMPLE.
Vo particles move in the circumference of a circle with constant ds of v and 2 v. Find their relative velocities. et the slower one be chosen as the reference particle, and let the angle Di, Fig. 53, be denoted by 6. Then the velocity of PI relative to P2 is
= 2 v and Vz = v, therefore
v V5 — 4 cos 0. P,
FIG. 53.
[SCUSSION. —Whenever PI passes P2 the value of 6 is a multiple of herefore cos 6 = 1 and v' = v. When the particles occupy the ends